The Origin of Broad Emission in ⟨100⟩ Two-Dimensional Perovskites: Extrinsic vs Intrinsic Processes

2D metal halide perovskites can show narrow and broad emission bands (BEs), and the latter’s origin is hotly debated. A widespread opinion assigns BEs to the recombination of intrinsic self-trapped excitons (STEs), whereas recent studies indicate they can have an extrinsic defect-related origin. Here, we carry out a combined experimental–computational study into the microscopic origin of BEs for a series of prototypical phenylethylammonium-based 2D perovskites, comprising different metals (Pb, Sn) and halides (I, Br, Cl). Photoluminescence spectroscopy reveals that all of the compounds exhibit BEs. Where not observable at room temperature, the BE signature emerges upon cooling. By means of DFT calculations, we demonstrate that emission from halide vacancies is compatible with the experimentally observed features. Emission from STEs may only contribute to the BE in the wide-band-gap Br- and Cl-based compounds. Our work paves the way toward a complete understanding of broad emission bands in halide perovskites that will facilitate the fabrication of efficient narrow and white light emitting devices.


DFT simulations
Electronic structure of (PEA) 2

SnI 4 and (PEA) 2 PbI 4
The impact of the level of theory on the electronic properties of 2D perovskites is illustrated in the following for the PEA 2 SnI 4 and PEA 2 PbI 4 phases. Calculations have been carried out on the relaxed structures of the phases obtained by using the PBE functional (DFT-D3 dispersions included) and by fixing cell parameters to the experimental values.
At the PBE level of theory, spin-orbit coupling (SOC) included, the PEA 2 SnI 4 and PEA 2 PbI 4 phases show direct band gaps at the Γ point in the Brillouin zone (BZ) of 1.32 eV and 0.99 eV, respectively, see Figure S3 and Table S1. Similar to the 3D bulk phase, the top of the valence band (VBM) is associated to I-p orbitals, while the conduction band minimum (CBM) is mainly associated with the p-states of the metal. As expected, the calculated band gaps at the PBE-SOC level are underestimated, as demonstrated by the higher optical band gaps measured in absorption experiments.
In order to provide a more accurate prediction of the optoelectronic properties of the phases, the band gaps of the PEA 2 PbI 4 and PEA 2 SnI 4 phases have been calculated by the G 0 W 0 method, by using the Yambo code. 1 In Table S1 the calculated band gaps at the G 0 W 0 -SOC level are reported. A renormalization of the band gaps to values of 1.88 and 2.51 eV is reported for PEA 2 SnI 4 and PEA 2 PbI 4 , respectively. The calculated band gaps are in good agreement with experimental works reporting values of 2.08 and 2.61 eV for PEA 2 SnI 4 and PEA 2 PbI 4 , respectively. 2 The accuracy of hybrid functionals in the description of the electronic structure of the phases has been checked by recalculating the band gaps at the PBE0-SOC level, see Table S1. A good agreement with G 0 W 0 calculations is found for lead, while for tin perovskite the band gap is slightly overestimated by the PBE0 functional. This analysis shows that PBE0 functional (SOC included) provides an accurate description of the electronic properties of these systems. Notably, small deviations of the calculated PBE0-SOC band gaps of PEA 2 SnI 4 and PEA 2 PbI 4 can be noticed between Table S1 and Table 1 of the main text. These variations are due to the slightly different structures of the phases obtained at the PBE and PBE0 levels of theory (band gaps reported in Table 1 of the main text have been calculated at the PBE0 relaxed structures obtained by the CP2K code).

Defect calculations
Defect formation energies (DFE) and thermodynamic ionization levels (TIL) of defects were calculated by using the following relations 3 where E[X q ] is the energy of the supercell with defect X in the charge state q; E(perf) is the energy of the perfect (non-defective) supercell; n and μ are, respectively, the number and the chemical potentials of the species added or subtracted to the non-defective system; ε VB and ε F are the valence band energy and the Fermi level; E q corr is the correction term due to the charge. Charge corrections have been applied by following the Makov-Payne scheme by using the ionic dielectric constant of the phases calculated at the PBE level by following the approach of Umari et al 4 (see Table S4).
The chemical potentials of the elements in the calculation of PEA 2 SnI 4 and PEA 2 PbI 4 DFEs have been set by imposing the thermodynamic stability of the 2D perovskites and the equilibrium between the 2D perovskites and the relative metal precursors (SnI 2 and PbI 2 ) The electronic structure analysis highlights that quantum confinement into two dimensions increases the band gap energy through a down/up-shift of the VBM/CBM for both tin and lead perovskites compared to their 3D counterparts (see Figure S4). At the PBE0 level of theory, spin-orbit corrections (SOC) included, a down-shift of 0.42 eV and an upshift of 0.45 eV are observed for the VBM and CBM of PEA 2 PbI 4 with respect to 3D MAPbI 3 (see Figure   S4 and Figure S5). Shifts of 0.59 and 0.25 eV of the VBM and CBM are observed in the case of PEA 2 SnI 4 . These shifts and the associated band gaps opening leads to a widening of the stability field of defects and to a deepening of the VB and CB-related ionization levels compared with 3D analogues. As an example, (+/0) levels of V I , which are shallow in